In a passive radar system, radio signals reflected or transmitted by a target object are received by multiple passive sensors geographically distributed. Passive sensors do not emit the radio signals that are reflected, as would be the case in an active radar system. The main problem with passive radar is that the relative timing of pulses in the received signals is unknown.
Usually, the passive sensors forward the received radio signals to a centralized processing unit. The processing unit performs a cross-correlation on pairs of signals to estimate a time-difference-of-arrival (TDOA) for pairs of the signals. The TDOA can then be used to determine the position of the target object.
FIG. 1 shows conventional cross-correlation processing. A first signal r1(t) 100 and a second signal r2(t) 101 are received at corresponding sensors geographically distributed. The radio signals were reflected or transmitted by a target object 105.
The signals can be forwarded to a centralized processing unit. At the processing unit, the first signal r1(t) 100 and the second signal r2(t) 101 are cross-correlated 110 over an entire correlation time interval T 102 according to a cross-correlation function R(x). Then, a peak detector 111 determines a peak of an absolute value x 103 of the cross-correlation function for the entire interval. The value x corresponds to the cross-correlation peak over the entire cross-correlation interval. The peak is then output as an estimate {circumflex over (θ)} 104 of the TDOA for signals r1(t) 100 and r2(t) 101.
Conventional cross-correlation processing evaluates a cross-correlation function for various delays between the signals to obtain the delay corresponding to a maximum cross-correlation value during the cross-correlation interval, i.e., a “peak.”
The conventional cross-correlation processing works adequately for single path channels and additive white Gaussian (random) noise (AWGN). However, that processing does not account for the phenomena of fading, frequency selectivity, interference, nonlinearity, terrain blocking and dispersion. Therefore, the performance can degrade significantly in multipath environments, and in the presence of non-white noise, as is frequently the case in terrestrial channels.
In order to improve the performance of the conventional cross-correlation, generalized cross-correlation (GCC) techniques have been developed. Instead of determining the maximum cross-correlation value between a pair of signals, GCC techniques first filter the input signals and then operate on filtered versions of the signals. The combined effect can be considered as shaping the cross-power spectral density (cross-PSD) of the received signals.
Various filtering functions can be considered for improving the performance in the presence of uncorrelated noise. As is known in the art, a filter performs a multiplication in the frequency domain.
Although the GCC filtering techniques can improve TDOA estimation, they are ineffective for multipath propagation, which causes correlated noise in the received signals. In order to reduce the effects of multipath propagation, adaptive estimation techniques have been described. However, those techniques can also fail when there are more than three multipath components.
The conventional cross-correlation technique to estimate TDOA can be expressed as a delay
                                                        θ              ^                        =                          arg              ⁢                                                          ⁢                                                max                  x                                ⁢                                                                        R                    ⁡                                          (                      x                      )                                                                                                                      ,                                          ⁢          where                ⁢                                  ⁢                              R            ⁡                          (              x              )                                =                                    ∫              0              T                        ⁢                                                            r                  1                                ⁡                                  (                  t                  )                                            ⁢                                                r                  2                                ⁡                                  (                                      t                    -                    x                                    )                                            ⁢                              ⅆ                t                                                                        (        1        )            is the cross-correlation function for the pair of signals r1(t) and r2(t), and T is the correlation time interval.
One problem with the conventional cross-correlation processing is that if the time interval T for the cross-correlation is not selected appropriately, i.e., longer than needed, extra noise can be accumulated. This is due to the nature of noise-noise cross-terms for low signal-to-noise ratios (SNRs).
In addition, in the presence of multipath propagation, multiple cross-correlation peaks can occur, which can increase the estimation error significantly. It is desired to solve these problems.